Related papers: Knot Solitons
The set of isotopy classes of nontrivial torus knots $T(p,q)$ in $S^3$ is in bijection with the set of coprime integer pairs $(p,q)$ satisfying $|p|>q\geq 2$. We verify the AJ conjecture for the connected sums $T(p,q)\# T(a,b)$ when $p$ and…
Nonlinear sigma models compatible with the aratyn-Ferreira-Zimerman ansatz are discussed, the latter ansatz automatically leading to configurations with definite values of the Hopf index. These models are allowed to involve a weight factor…
This paper concerns pseudo-classical knots in the non-orientable manifold $\hat{\Sigma} =\Sigma \times [0,1]$, where $\Sigma$ is a non-orientable surface and a knot $K \subset \hat{\Sigma}$ is called pseudo-classical if $K$ is…
A framework for studying knot and link invariants from any rational conformal field theory is developed. In particular, minimal models, superconformal models and $W_N$ models are studied. The invariants are related to the invariants…
In this paper, we study topological concordance modulo local knotting, or almost-concordance, of knots in 3-manifolds $M\neq S^3$. A. Levine, Celoria (arXiv:1602.05476v4), and Friedl-Nagel-Orson-Powell (arXiv:1611.09114v2) conjecture that,…
The possibility of interpreting baryons containing a single heavy quark as bound states of solitons (that arise in the nonlinear sigma model) and heavy mesons is explored. Particular attention is paid to the parity of the bound states and…
Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants…
Two topological issues on membranes in M-theory are studied: (1) Soliton is an important subject in M-theory. Under the framework of obstruction theory with the help from framed links in $S^3$, we give a complete enumeration of topological…
By methods of numerical simulation the interaction of 180-degree domain walls with oscillating solitons in (2+1)-dimensional O(3) nonlinear sigma model is investigated. A model of the collisions in which there is observed a reflection of…
We show that the degeneracy of topological solitons in the gauged O(3) non-linear sigma model with Chern-Simons term may be removed by chosing a self-interaction potential with symmetry - breaking minima. The topological solitons in the…
This survey explores knot polynomials and their categorification, culminating in the homological invariants of knots. We begin with an overview of classical knot polynomials, progressing towards the superpolynomial and its role in unifying…
We construct meta-stable knotted domain strings on the surface of a soliton of the shape of a torus in 3+1 dimensions. We consider the simplest case of Z2 Wess-Zumino-type domain walls for which we can cover the torus with a domain string…
We show that perturbing the definition of sl(n) Khovanov-Rozansky link homology gives a lower bound on the slice genus of a knot. As a corollary this yields another proof of Milnor's conjecture on the slice genus of torus knots.
We define Floer homology theories for oriented, singular knots in S^3 and show that one of these theories can be defined combinatorially for planar singular knots.
We classify all finite group actions on knots in the 3-sphere. By geometrization, all such actions are conjugate to actions by isometries, and so we may use orthogonal representation theory to describe three cyclic and seven dihedral…
Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have…
Topological terms in the O(3) nonlinear sigma model in (1+1) and (2+1) dimensions are re-examined based on the description of the SU(2)-valued field $g$. We first show that the topological soliton term in (1+1) dimensions arises from the…
We consider the space of all smooth knots in the 3-sphere isotopic to a given knot, with the aim of finding a small subspace onto which this large space deformation retracts. For torus knots and many hyperbolic knots we show the subspace…
The non-orientable 4-genus of a knot $K$ in $S^{3}$, denoted $\gamma_4(K)$, measures the minimum genus of a non-orientable surface in $B^{4}$ bounded by $K$. We compute bounds for the non-orientable 4-genus of knots $T_{5, q}$ and $T_{6,…
As a first step to understand how complicated attractors for dynamical systems can be, one may consider the following realizability problem: given a continuum $K \subseteq \mathbb{R}^3$, decide when $K$ can be realized as an attractor for a…